Theorems · Theorem · Lie groups
OpenSubgroup.isClosed
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] (U : OpenSubgroup G),
IsClosed ↑U- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- HasQuotient.Quotientproof · cited by 2,301
- IsClosedstatement · cited by 1,639
- DiscreteTopologyproof · cited by 373
- SeparatelyContinuousMulstatement and proof · cited by 133
- OpenSubgroupstatement and proof · cited by 47
- OpenSubgroup.toSubgroupproof · cited by 34
- OpenSubgroup.isOpenproof · cited by 7
- QuotientGroup.discreteTopologyproof · cited by 2
- QuotientGroup.t1Space_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.isClosed_of_isOpenproof · cited by 2
- IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_oneproof · cited by 1
- OpenSubgroup.isClopenproof · cited by 0
- IntermediateField.fixingSubgroup_isClosedproof · cited by 0